# Chapter 30:Speed Control of D.C. Motors¶

## Example Number 30.1, Page Number:1032¶

In [3]:
#variable declaration
v=500#V
n=250#rpm
ia=200#A
ra=0.12#ohm
ratio=0.80
ia2=100#A

#calculations
eb1=v-ia*ra
eb2=v-ia2*ra
n2=eb2*n/(eb1*ratio)

#result
print "speed=",round(n2),"rpm"

speed= 320.0 rpm


## Example Number 30.2, Page Number:1032¶

In [8]:
#variable declaration
v=250#V
ra=0.25#ohm
ia=50#A
n=750#rpm
ratio=1-0.10

#calculation
ia2=ia/ratio
eb1=v-ia*ra
eb2=v-ia2*ra
n2=eb2*n/(eb1*ratio)

#result
print "speed=",round(n2),"rpm"

speed= 828.0 rpm


## Example Number 30.3, Page Number:1032¶

In [19]:
#variable declaration
v=230.0#V
n=800#rpm
ia=50.0#A
n2=1000#rpm
ia2=80.0#A
ra=0.15#ohm
rf=250.0#ohm

#calculation
eb1=v-ia*ra
eb2=v-ia2*ra
ish1=v/rf
r1=(n2*eb1*v)/(n*eb2*ish1)
r=r1-rf
ish2=v/r1
torque_ratio=ish2*ia2/(ish1*ia)

#result
print "ratio of torque=",torque_ratio

resistance to be added= 68.9506880734 ohm
ratio of torque= 1.25411235955


## Example Number 30.3, Page Number:1033¶

In [23]:
#variable declaration
v=250.0#V
rf=250.0#ohm
ra=0.25#ohm
n=1500#rpm
ia=20.0#A
r=250.0#ohm

#calculations
ish=v/rf
ish2=v/(rf+r)
ia2=ia*1/ish2
eb2=v-ia2*ra
eb1=v-ia*ra
n2=eb2*n/(eb1*ish2)

#result
print "new speed=",round(n2),"rpm"
print "new armature current=",ia2,"A"

new speed= 2939.0 rpm
new armature current= 40.0 A


## Example Number 30.5, Page Number:1033¶

In [37]:
import math
from sympy.solvers import solve
from sympy import Symbol
#variable declaration
rt=Symbol('rt')
v=250.0#V
ra=0.5#ohm
rf=250.0#ohm
n=600.0#rpm
ia=20.0#A
n2=800.0#rpm

#calculation
ish1=v/rf
eb1=v-ia*ra
rt=solve(((n2*eb1*(v/rt))/(n*(v-(ia*ra/(v/rt)))))-1,rt)
r=rt[0]-rf

#result
print "resistance to be inserted=",r,"ohm"

resistance to be inserted= 88.3128987990058 ohm


## Example Number 30.6, Page Number:1034¶

In [38]:
import math
from sympy.solvers import solve
from sympy import Symbol
#variable declaration
x=Symbol('x')
v=220#V
ra=0.5#ohm
ia=40#A
ratio=1+0.50

#calculation
eb1=v-ia*ra
x=solve((ratio*eb1/((v-ia*ra*x)*x))-1,x)
per=1-1/x[0]

#result
print"main flux has to be reduced by=",per*100,"%"

main flux has to be reduced by= 37.2991677469778 %


## Example Number 30.7, Page Number:1034¶

In [40]:
#variable declaration
v=220#V
i=41#A
ra=0.2#ohm
rw=0.05#ohm
ri=0.1#ohm
rf=110#ohm
ratio=1-0.25
r=1#ohm
ratio1=1-0.50
n=2500
#calculation
ish=v/rf
ia1=i-ish
ia2=ratio1*ia1/ratio
eb1=v-ia1*(ra+ri+rw)
eb2=v-ia2*(r+ra+ri+rw)
n2=eb2*n/(eb1*ratio)

#result
print "armature current=",ia2,"A"
print "motor speed=",round(n2),"rpm"

armature current= 26.0 A
motor speed= 2987.0 rpm


## Example Number 30.8, Page Number:1035¶

In [46]:
#variable declaration
v=220#V
n=850#rpm
ia=72.2#A
ra=0.25#ohm
rf=100#ohm
n2=1650#rpm
ia2=40#A

#calculation
ish=v/rf
ia1=ia-ish
eb1=v-ia1*ra
eb2=v-ia2*ra
ratio=(n*eb2)/(n2*eb1)
per=1-ratio
#result
print "percentage reduction=",per*100,"%"

percentage reduction= 46.5636857585 %


## Example Number 30.9, Page Number:1035¶

In [49]:
import math
from sympy.solvers import solve
from sympy import Symbol
#variable declaration
ia2=Symbol('ia2')
v=220#V
ra=0.5#ohm
ia=40#A
ratio=0.50+1

#calculation
eb1=v-ia*ra
ia2=solve((((v-ra*ia2)*ia2)/(eb1*ratio*ia))-1,ia2)
per=ia/ia2[0]

#result
print "mail flux should be reduced by=",round(per,4)*100,"%"

mail flux should be reduced by= 62.7 %


## Example Number 30.10, Page Number:1035¶

In [53]:
#variable declaration
ia=20.0#A
v=220.0#V
ra=0.5#ohm
ratio=0.50

#calculation
eb1=v-ia*ra
eb2=ratio*(v-ia*ra)
r=(v-eb2)/ia-ra

#result
print "resistance required in the series=",r,"ohm"

resistance required in the series= 5.25 ohm


## Example Number 30.11, Page Number:1036¶

In [55]:
#variable declaration
v=250#V
n=1000#rpm
ia=8#A
i_f=1#A
ra=0.2#ohm
rf=250#ohm
i=50#A

#calculations
eb0=v-(ia-i_f)*ra
kpsi=eb0/1000
ia=i-i_f
eb1=v-ia*ra
n1=eb1/kpsi

#result
print "speed=",round(n1,1),"rpm"

speed= 966.2 rpm


## Example Number 30.12, Page Number:1037¶

In [61]:
#variable declaration
v=240#V
ra=0.25#ohm
n=1000#rpm
ia=40#A
n2=800#rpm
i2=20#A
#calculation
eb=v-ia*ra
eb2=n2*eb/n
r=(v-eb2)/(ia)-ra
eb3=v-i2*(r+ra)
n3=eb3*n/eb

#result
print "speed=",round(n3),"rpm"

additional resistance= 1.15 ohm
speed= 922.0 rpm


## Example Number 30.13, Page Number:1037¶

In [81]:
#variable declaration
v=220#V
n=990#rpm
efficiency=0.88
ra=0.08#ohm
ish=2#A
n2=450#rpm

#calculation
i=input_p/v
ia=i-ish
loss=v*ish
cu_loss=ia**2*ra
loss_nl=losses-cu_loss-loss
eb1=v-20-(ia*ra)
eb2=n2*eb1/n
r=(eb1-eb2)/ia
total_loss=ia**2*(r+ra)+loss+loss_nl
output=input_p-total_loss
efficiency=output/(input_p)

#result
print "motor input=",input_p/1000,"kW"
print "armature current=",ia,"A"
print "external resistance=",r,"ohm"
print "efficiency=",efficiency*100,"%"

motor input= 8.5 kW
armature current= 36.6363636364 A
external resistance= 2.93403113016 ohm
efficiency= 41.6691237902 %


## Example Number 30.14, Page Number:1038¶

In [83]:
#variable declaration
eb1=230.0#V
n=990.0#rpm
n2=500.0#rpm
ia=25.0#A

#calculation
eb2=eb1*n2/n
r=(eb1-eb2)/ia

#result
print "resistance required in series=",r,"ohm"

resistance required in series= 4.55353535354 ohm


## Example Number 30.15, Page Number:1038¶

In [90]:
#variable declaration
v=220.0#V
ra=0.4#ohm
rf=200.0#ohm
ia=20.0#A
n=600.0#rpm
n2=900.0#rpm

#calculation
if1=v/rf
eb1=v-ia*ra
k2=eb1/(if1*n)
if2=n*if1/n2
rf1=v/if1
rf2=v/if2
r=rf2-rf1

#result

resistance to be added= 100.0 ohm


## Example Number 30.16, Page Number:1039¶

In [103]:
import math
from sympy.solvers import solve
from sympy import Symbol
#variable declaration
ia2=Symbol('ia2')
v=220.0#V
ra=0.4#ohm
rf=200.0#ohm
ia=22.0#A
n=600.0#rpm
n2=900.0#rpm

#calculation
if1=v/rf
eb1=v-ia*ra
k1=eb1/(if1*n)
if2=n*if1/n2
if2=n2*ia/n
ia2=solve(v-ra*ia2-(k1*ia*if1*n2)/ia2,ia2)
if2=ia*if1/ia2[0]
r=v/if2

#result
print "new field resistance to be added=",r,"ohm"

new field resistance to be added= 306.828780053869 ohm


## Example Number 30.17, Page Number:1040¶

In [105]:
#variable declaration
v=250#V
output=25#kW
efficiency=0.85
n=1000#rpm
ra=0.1#ohm
rf=125#ohm
ratio=1.50

#calculation
input_p=output*1000/efficiency
i=input_p/v
if1=v/rf
ia=i-if1
il=ratio*ia
r=v/il
r_ext=r-ra

#result
print "starting resistance=",round(r_ext,3),"ohm"

starting resistance= 1.341 ohm


## Example Number 30.18, Page Number:1042¶

In [111]:
#variable declaration
v=200.0#V
n=1000.0#rpm
ia=17.5#A
n2=600.0#rpm
ra=0.4#ohm

#calculation
eb1=v-ia*ra
rt=(v-(n2*eb1/n))/ia
r=rt-ra
#result
print "resistance to be inserted=",round(r,1),"ohm"

resistance to be inserted= 4.4 ohm


## Example Number 30.19, Page Number:1042¶

In [113]:
#variable declaration
v=500#V
ra=1.2#ohm
rf=500#ohm
ia=4#A
n=1000#rpm
i=26#A
r=2.3#ohm
ratio=0.15

#calculation
ish=v/rf
ia1=ia-ish
eb1=v-ia1*ra
ia2=i-ish
eb2=v-ia2*ra
n2=n*eb2/eb1
eb2=v-ia2*(r+ra)
n2_=n*eb2/eb1
n2__=n*eb2/(eb1*(1-ratio))

#result
print "speed when resistance 2.3 ohm is connected=",round(n2_),"rpm"
print "speed when shunt field is reduced by 15%=",round(n2__),"rpm"

speed when resistance 2.3 ohm is connected= 831.0 rpm
speed when shunt field is reduced by 15%= 978.0 rpm


## Example Number 30.20, Page Number:1043¶

In [117]:
#variable declaration
v=250.0#V
ia1=ia2=20.0#A
n=1000.0#rpm
ra=0.5#ohm
n2=500.0#ohm

#calculation
eb1=v-ia1*ra
rt=(v-((n2/n)*eb1))/ia2
r=rt-ra
ia3=ia2/2
n3=n*(v-ia3*rt)/eb1
#result
print "speed=",round(n3),"rpm"

speed= 771.0 rpm


## Example Number 30.21, Page Number:1043¶

In [137]:
#variable declaration
v=250.0#V
ra1=0.5#ohm
n=600.0#rpm
ia2=ia1=20#A
r=1.0#ohm

#calculations
eb1=v-ia1*ra1
ra2=r+ra1
eb2=v-ia2*ra2
n2=eb2*n/eb1
#torque is half the full-load torque
ia2=1.0/2.0*ia1
eb22=v-ia2*ra2
n2_=eb22*n/eb1
#result
print "speed at full load torque=",round(n2),"rpm"
print "speed at half full-load torque=",round(n2_),"rpm"

speed at full load torque= 550.0 rpm
speed at half full-load torque= 588.0 rpm


## Example Number 30.22, Page Number:1044¶

In [142]:
#variable declaration
v=220.0#V
ra1=0.5#ohm
n=500.0#rpm
ia2=ia1=30.0#A
r=1.0#ohm

#calculations
eb1=v-ia1*ra1
ra2=r+ra1
eb2=v-ia2*ra2
n2=eb2*n/eb1

#torque is half the full-load torque
ia2=2.0*ia1
eb22=v-ia2*ra2
n2_=eb22*n/eb1
#result
print "speed at full load torque=",round(n2),"rpm"
print "speed at double full-load torque=",round(n2_),"rpm"

speed at full load torque= 427.0 rpm
speed at double full-load torque= 317.0 rpm


## Example Number 30.23, Page Number:1044¶

In [157]:
#variable declaration
v=500.0#V
n=750.0#rpm
efficiency=0.90
t2=250.0#N-m
r=5.0#ohm
ra=0.5#ohm

#calculation
ia2=ia1*math.sqrt(t2/t1)
eb1=v-ia1*ra
eb2=v-ia2*(r+ra)
n2=eb2*ia1*n/(eb1*ia2)

#result
print "speed at which machine will run=",round(n2),"rpm"

speed at which machine will run= 381.789716486 rpm


## Example Number 30.24, Page Number:1044¶

In [175]:
#variable declaration
output=7.46*1000#W
v=220.0#V
n=900.0#rpm
efficiency=0.88
ra=0.08#ohm
ish=2.0#A
n2=450.0#rpm
#calculation
i=output/(efficiency*v)
ia2=ia1=i-ish
eb1=v-ia2*ra
rt=(v-20-((n2/n)*eb1))/ia2
r=rt-ra
input_m=(v)*(ia2+ish)
total_loss=input_m-output
cu_loss=ia2**2*ra
cu_loss_f=v*ish
total_cu_loss=cu_loss+cu_loss_f
stray_loss=total_loss-total_cu_loss
stray_loss2=stray_loss*n2/n
cu_loss_a=ia1**2*rt
total_loss2=stray_loss2+cu_loss_f+cu_loss_a
output2=input_m-total_loss2
efficiency=output2*100/input_m

#result
print "motor output=",output2,"W"
print "armature current=",ia2,"A"
print "external resistance=",r,"ohm"
print "overall efficiency=",efficiency,"%"

motor output= 4460.66115702 W
armature current= 36.5330578512 A
external resistance= 2.42352222599 ohm
overall efficiency= 52.619059225 %


## Example Number 30.25, Page Number:1044¶

In [187]:
#variable declaration
v=240.0#V
ia=15.0#A
n=800.0#rpm
ra=0.6#ohm
n2=400.0#rpm

#calculation
eb1=v-ia*ra
r=((v-(n2*eb1/n))/ia)-ra
ia3=ia/2
eb3=v-ia3*(r+ra)
n3=eb3*n/eb1

#result
print "speed=",n3,"rpm"

speed= 615.584415584 rpm


## Example Number 30.26, Page Number:1045¶

In [14]:
import math
from sympy.solvers import solve
from sympy import Symbol
#variable declaration
r=Symbol('r')
v=400.0#V
inl=3.5#A
il=59.5#A
rf=267.0#ohm
ra=0.2#ohm
vd=2.0#V
ratio=0.02
speed_ratio=0.50

#calculations
ish=v/rf
ia1=inl-ish
eb1=v-ia1*ra-vd
ia2=il-ish
eb2=v-ia2*ra-vd
n1_by_n2=eb1*(1-ratio)/eb2
per_change=(1-1/n1_by_n2)*100
r=solve(eb2*speed_ratio/(eb2-ia2*r)-1,r)
#result
print "change in speed=",per_change,"%"

change in speed= 0.83357557339 %
resistance to be added= 3.33092370774547 ohm


## Example Number 30.27, Page Number:1046¶

In [16]:
#variable declaraion
v=200.0#V
i=50.0#A
n=1000.0#rpm
n2=800.0#rpm
ra=0.1#ohm
rf=100.0#ohm

#calculations
ish=v/rf
ia1=i-ish
ia2=ia1*(n2/n)**2
eb1=v-ia1*ra
eb2=v-ia2*ra
rt=(v-(n2*eb1/n))/ia2
r=rt-ra
#result
print "resustance that must be added=",r,"ohm"

resustance that must be added= 1.32708333333 ohm


## Example Number 30.28, Page Number:1047¶

In [22]:
#variable declaration
v=250#V
efficiency=0.90
n=1000#rpm
ra=0.1#ohm
rf=115#ohm
ratio=1.5

#calculation
ish=v/rf
ia=i-ish
eb=v-ia*ra
ta=9.55*eb*ia/n
i_permissible=i*ratio
ia_per=i_permissible-ish
ra_total=v/ia_per
r_required=ra_total-ra
torque=ratio*ta
#result
print "net torque=",ta,"N-m"
print "starting resistance=",r_required,"ohm"
print "torque developed at starting=",torque,"N-m"

net torque= 365.403326173 N-m
starting resistance= 0.913513513514 ohm
torque developed at starting= 548.104989259 N-m


## Example Number 30.29, Page Number:1047¶

In [36]:
import math
from sympy.solvers import solve
from sympy import Symbol
#variable declaration
I=Symbol('I')
v=200.0#V
rf=40.0#ohm
ra=0.02#ohm
i=55.0#A
n=595.0#rpm
r=0.58#ohm
n2=630.0#rpm
ia_=15.0#A
rd=5.0#ohm
ia2=50.0#A

#calculation
ish=v/rf
ia1=i-ish
ra1=r+ra
eb1=v-ra1*ia1
ia2=ia1
eb2=eb1*(n2/n)
r=(v-eb2)/ia1
eb2_=v-ia_*ra1
n2=eb2_*n/eb1
eb3=eb1
IR=v-eb3-ia2*ra
pd=v-IR
i_d=pd/rd
i=ia2+i_d
R=IR/i
I=solve(rd*(I-ia_)-v+R*I,I)
eb4=v-R*I[0]-ia_*ra
n4=n*(eb4/eb1)

#result
print "armature circuit resistance should be reduced by=",ra1-r,"ohm"
print "speed when Ia=",n2,"rpm"
print "value of series resistance=",R,"ohm"
print "speed when motor current falls to 15A=",n4,"rpm"

armature circuit resistance should be reduced by= 0.2 ohm
speed when Ia= 668.5 rpm
value of series resistance= 0.344418052257 ohm
speed when motor current falls to 15A= 636.922222222222 rpm


## Example Number 30.31, Page Number:1051¶

In [37]:
import math
#variable declaration
i=15#A
n=600#rpm

#calculation
ia2=math.sqrt(2*2**0.5*i**2)
n2=n*2*i/ia2

#result
print "speed=",n2,"rpm"
print "current=",ia2,"A"

speed= 713.524269002 rpm
current= 25.2268924576 A


## Example Number 30.32, Page Number:1052¶

In [44]:
#variable declaration
n=707#rpm
ia1=100#A
v=85#V
rf=0.03#ohm
ra=0.04#ohm

#calculation
ra_total=ra+(2*rf)
eb1=v-ia1*ra_total
ia2=ia1*2**0.5
rf=rf/2
eb2=v-ia2*(ra+rf)
n2=n*(eb2/eb1)*(2*ia1/ia2)
rt=(v-((n/n2)*eb2))/ia2
r=rt-ra-rf

#result
print "speed=",n2,"rpm"

speed= 1029.46885374 rpm


## Example Number 30.33, Page Number:1052¶

In [49]:
#varable declaration
v=240.0#V
ia=40.0#A
ra=0.3#ohm
n=1500.0#rpm
n2=1000.0#rpm
#calculation
R=v/ia-ra
eb1=v-ia*ra
r=(v-((n2/n)*eb1))/ia-ra

#result
print "resistance to be added at starting=",R,"ohm"
print "resistance to be added at 1000 rpm",r,"ohm"

resistance to be added at starting= 5.7 ohm
resistance to be added at 1000 rpm 1.9 ohm


## Example Number 30.34, Page Number:1053¶

In [50]:
#variable declaration
n=600.0#rpm
v=250.0#V
ia1=20.0#A
ratio=2.0

#calculations
ia2=ia1*2**(3.0/4.0)
n2=n*ratio*ia1/ia2

#result
print "current=",ia2,"A"
print "speed=",n2,"rpm"

current= 33.6358566101 A
speed= 713.524269002 rpm


## Example Number 30.35, Page Number:1053¶

In [58]:
import math
from sympy.solvers import solve
from sympy import Symbol
#variable declaration
V=Symbol('V')
ra=1.0#ohm
v=220.0#V
n=350.0#rpm
ia=25.0#A
n2=500.0#rpm

#calculation
ia2=ia*(n2/n)
eb1=v-ia*ra
V=solve((n2*eb1*ia2/(n*ia))+ia2-V,V)

#result
print " current=",ia2,"A"
print "voltage=",V[0],"V"

 current= 35.7142857143 A
voltage= 433.673469387755 V


## Example Number 30.36, Page Number:1053¶

In [61]:
#variable declaration
n=1000.0#rpm
ia=20.0#A
v=200.0#V
ra=0.5#ohm
rf=0.2#ohm
i=20.0#A
rd=0.2#ohm
i_f=10.0#A
ratio=0.70

#calculation
eb1=v-(ra+rf)*ia
r_total=ra+rf/2
eb2=v-r_total*ia
n2=(eb2*n/(eb1*ratio))

#result
print "speed=",round(n2),"rpm"

speed= 1444.0 rpm


## Example Number 30.37, Page Number:1054¶

In [63]:
#variable declaration
v=200.0#V
ia=40.0#A
n=700.0#rpm
ratio=0.50+1
ra=0.15#ohm
rf=0.1#ohm

#calculations
ia2=(ratio*2*ia**2)**0.5
eb1=v-ia*(ra+rf)
eb2=v-ia2*(ra+rf)
n2=(eb2/eb1)*(ia*2/ia2)*n

#result
print "speed=",n2,"rpm"
print "speed=",ia2,"A"

speed= 777.147765122 rpm
speed= 69.2820323028 A


## Example Number 30.38, Page Number:1055¶

In [74]:
#variable declaration
v=250#V
ia=20#A
n=900#rpm
r=0.025#ohm
ra=0.1#ohm
rd=0.2#ohm

#calculation
eb1=v-ia*(ra+4*r)
ia2=(ia**2*(ra+rd)/rd)**0.5
ra_=rd*ra/(ra+rd)
eb2=v-ia2*ra_
n2=(eb2/eb1)*(ia*3/(2*ia2))*n

#rearranged field coils in two series and parallel group
ia2=(ia**2*2)**0.5
r=ra+r
eb2=v-ia2*r
n2_=(eb2/eb1)*(ia*2/(ia2))*n

#result
print "speed when divertor was added=",n2,"rpm"
print "speed when field coils are rearranged=",n2_,"rpm"

speed when divertor was added= 1112.87640676 rpm
speed when field coils are rearranged= 1275.19533144 rpm


## Example Number 30.39, Page Number:1055¶

In [75]:
#variable declaration
v=230.0#V
n=1000.0#rpm
i=12.0#A
rf=0.8#ohm
ra=1.0#ohm
il=20#A
ratio=0.15

#calculation
eb1=v-i*(ra+rf)
eb2=v-il*(ra+rf/4)
n2=(eb2/eb1)*(1/(1-ratio))*n

#result
print "speed=",n2,"rpm"

speed= 1162.92198261 rpm


## Example Number 30.40, Page Number:1056¶

In [97]:
import math
from sympy.solvers import solve
from sympy import Symbol
#variable declaration
i2=Symbol('i2')
v=200.0#v
n=500.0#rpm
i=25.0#A
ra=0.2#ohm
rf=0.6#ohm
rd=10.0#ohm

#calculation
r=ra+rf
eb1=v-i*r
i2=solve(((rd+rf)*i2**2)-(v*i2)-(i**2*rd),i2)
pd=v-i2[1]*rf
ia2=((rd+rf)*i2[1]-v)/rd
eb2=pd-ia2*ra
n2=(eb2/eb1)*(i/i2[1])*n
#result
print "speed=",n2,"rpm"

speed= 342.848235418389 rpm


## Example Number 30.41, Page Number:1056¶

In [99]:
#variable declaration
v=440#V
ra=0.3#ohm
i=20#A
n=1200#rpm
r=3#ohm
i2=15#A
ratio=0.80

#calculation
eb1=v-i*ra
eb2=v-(r+ra)*i2
n2=n*(eb2/eb1)/ratio
power_ratio=(n*i)/(n2*i2*ratio)

#result
print "new speed=",n2,"rpm"
print "ratio of power outputs=",power_ratio

new speed= 1349.65437788 rpm
ratio of power outputs= 1.48186086214


## Example Number 30.42, Page Number:1057¶

In [103]:
#variable declaration
i=50#A
v=460#V
ratio=1-0.25

#calculation
I=(i**2*ratio**3)**0.5
eb2=I*ratio*v/i
R=(v-eb2)/I
pa=v*i/1000
power_n=pa*ratio**4
pa=eb2*I

#result
print "Resistance required=",R,"ohm"

Resistance required= 7.26432660412 ohm


## Example Number 30.44, Page Number:1060¶

In [109]:
#variable declaration
n=500#rpm
n2=550#rpm
i=50#A
v=500#V
r=0.5#ohm

#calculation
eb1=v-i*r
kphi1=eb1/n
eb2=v-i*r
kphi2=eb2/n2
eb_=v-i*2*r
n=eb_/((eb1/n2)+(eb2/n))
#result
print "speed=",n,"rpm"

speed= 248.120300752 rpm


## Example Number 30.45, Page Number:1061¶

In [117]:
#variable declaration
v=250#V
n=1000#rpm
ratio1=5.0
ratio2=4.0
t=882#N-m

#calculation
k=v/(n*i/60)
I=(t/((ratio1+ratio2)*0.159*k))**0.5
nsh=v/((ratio1+ratio2)*k*I)
eb1=ratio1*k*I*nsh
eb2=ratio2*k*I*nsh

#result
print "current=",I,"A"
print "speed of shaft=",round(nsh*60),"rpm"
print "voltage across the motors=",round(eb1),"V,",round(eb2),"V"

current= 49.5202984449 A
speed of shaft= 134.0 rpm
voltage across the motors= 139.0 V, 111.0 V


## Example Number 30.46, Page Number:1063¶

In [118]:
#variable declaration
v=220#V
t=700#N-m
n=1200#rpm
ra=0.008#ohm
rf=55#ohm
efficiency=0.90
t2=375#N-m
n2=1050#rpm

#calculation
output=2*3.14*n*t/60
power_m=output/efficiency
im=power_m/v
ish=v/rf
ia1=im-ish
eb1=v-ia1*ra
ia2=ia1*t2/t
eb2=eb1*n2/n
r=eb2/ia2-ra

#result
print "dynamic break resistance=",r,"ohm"

dynamic break resistance= 0.795525014538 ohm


## Example Number 30.47, Page Number:1064¶

In [122]:
#variable declaration
v=400.0#V
n=450.0#rpm
efficiency=0.746
ra=0.2#ohm

#calculations
eb=v-I*ra
vt=v+eb
i_max=2*I
r=vt/i_max
R=r-ra
N=n/60
phizp_by_a=eb/N
k4=phizp_by_a*v/(2*3.14*r)
k3=phizp_by_a**2/(2*3.14*r)
tb=k4+k3*N
tb0=k4
#result
print "breaking resistance=",R,"ohm"
print "maximum breaking torque=",tb,"N-m"
print "maximum breaking torque when N=0 =",tb0,"N-m"

breaking resistance= 6.1 ohm
maximum breaking torque= 1028.3970276 N-m
maximum breaking torque when N=0 = 522.360394972 N-m


## Example Number 30.48, Page Number:1069¶

In [124]:
#variable declaration
v=120#V
ra=0.5#ohm
l=20*0.001#H
ka=0.05#V/rpm motor constant
ia=20#A

#calculations
vt=ia*ra
alpha=vt/v
#when alpha=1
eb=v-ia*ra
N=eb/ka

#result
print "range of speed control=",0,"to",N,"rpm"
print "range of duty cycle=",(alpha),"to",1

 range of speed control= 0 to 2200.0 rpm
range of duty cycle= 0.0833333333333 to 1


## Example Number 30.49, Page Number:1080¶

In [125]:
#variable declaration
v=200#V
efficiency=0.85
ra=0.25#ohm
ratio=1.5

#calculation
i1=ratio*i
r1=v/i1
r_start=r1-ra
eb1=v-i*r1

#result
print "starting resistance=",r_start,"ohm"
print "back emf=",eb1,"V"

starting resistance= 2.78842716711 ohm
back emf= 66.6666666667 V


## Example Number 30.50, Page Number:1080¶

In [132]:
#variable declaration
v=220.0#V
ra=0.5#ohm
ia=40.0#A
n=7

#calculations
r1=v/ia
k=(r1/ra)**(1.0/(n-1))
r2=r1/k
r3=r2/k
r4=r3/k
r5=r4/k
r6=r5/k
p1=r1-r2
p2=r2-r3
p3=r3-r4
p4=r4-r5
p5=r5-r6
p6=r6-ra

#result
print "resistance of 1st section=",round(p1,3),"ohm"
print "resistance of 2nd section=",round(p2,3),"ohm"
print "resistance of 3rd section=",round(p3,3),"ohm"
print "resistance of 4th section=",round(p4,3),"ohm"
print "resistance of 5th section=",round(p5,3),"ohm"
print "resistance of 6th section=",round(p6,3),"ohm"

resistance of 1st section= 1.812 ohm
resistance of 2nd section= 1.215 ohm
resistance of 3rd section= 0.815 ohm
resistance of 4th section= 0.546 ohm
resistance of 5th section= 0.366 ohm
resistance of 6th section= 0.246 ohm


## Example Number 30.51, Page Number:1081¶

In [146]:
#variable declaration
n=6
v=200#V
ratio=0.50
i1=0.6#A
efficiency=0.88

#calculation
cu_loss=total_loss*ratio
i=output*1000/v
ia=i-i1
ra=cu_loss*1000/ia**2
i_per=i*2
ia_per=i_per-i1
r1=v/ia_per
k=(r1/ra)**(1.0/(n-1))
r2=r1/k
r3=r2/k
r4=r3/k
r5=r4/k
p1=r1-r2
p2=r2-r3
p3=r3-r4
p4=r4-r5
p5=r5-ra

#result
print "resistance of 1st section=",round(p1,3),"ohm"
print "resistance of 2nd section=",round(p2,3),"ohm"
print "resistance of 3rd section=",round(p3,3),"ohm"
print "resistance of 4th section=",round(p4,3),"ohm"
print "resistance of 5th section=",round(p5,3),"ohm"

resistance of 1st section= 1.627 ohm
resistance of 2nd section= 1.074 ohm
resistance of 3rd section= 0.709 ohm
resistance of 4th section= 0.468 ohm
resistance of 5th section= 0.309 ohm


## Example Number 30.52, Page Number:1081¶

In [157]:
#variable declaration
n=7
v=400#V
ratio=0.05
rsh=200#ohm
efficiency=0.92

#calculation
cu_loss=input_m*ratio
cu_loss_sh=v**2/rsh
cu_loss_a=cu_loss-cu_loss_sh
i=input_m/v
ish=v/rsh
ia=i-ish
ra=cu_loss_a/ia**2
k=(v/(ia*ra))**(1.0/(n))
i1=k*ia
r1=v/i1
r2=r1/k
r3=r2/k
r4=r3/k
r5=r4/k
r6=r5/k
r7=r5/k
p1=r1-r2
p2=r2-r3
p3=r3-r4
p4=r4-r5
p5=r5-r6
p6=r6-r7
p7=r7-ra

#result
print "resistance of 1st section=",round(p1,3),"ohm"
print "resistance of 2nd section=",round(p2,3),"ohm"
print "resistance of 3rd section=",round(p3,3),"ohm"
print "resistance of 4th section=",round(p4,3),"ohm"
print "resistance of 5th section=",round(p5,3),"ohm"
print "resistance of 6th section=",round(p6,3),"ohm"
print "resistance of 7th section=",round(p7,3),"ohm"

resistance of 1st section= 0.974 ohm
resistance of 2nd section= 0.592 ohm
resistance of 3rd section= 0.36 ohm
resistance of 4th section= 0.219 ohm
resistance of 5th section= 0.133 ohm
resistance of 6th section= 0.0 ohm
resistance of 7th section= 0.081 ohm


## Example Number 30.53, Page Number:1082¶

In [163]:
import math
from sympy.solvers import solve
from sympy import Symbol
#variable declaration
n=Symbol('n')
v=250.0#V
ra=0.125#ohm
i2=150.0#A
i1=200.0#A

#calculation
r1=v/i1
n=solve((i1/i2)**(n-1)-(r1/ra),n)
k=i1/i2
r2=r1/k
r3=r2/k
r4=r3/k
r5=r4/k
r6=r5/k
r7=r6/k
r8=r7/k
p1=r1-r2
p2=r2-r3
p3=r3-r4
p4=r4-r5
p5=r5-r6
p6=r6-r7
p7=r7-r8
p8=r8-ra
#result
print "resistance of 1st section=",round(p1,3),"ohm"
print "resistance of 2nd section=",round(p2,3),"ohm"
print "resistance of 3rd section=",round(p3,3),"ohm"
print "resistance of 4th section=",round(p4,3),"ohm"
print "resistance of 5th section=",round(p5,3),"ohm"
print "resistance of 6th section=",round(p6,3),"ohm"
print "resistance of 7th section=",round(p7,3),"ohm"
print "resistance of 8th section=",round(p8,3),"ohm"

resistance of 1st section= 0.313 ohm
resistance of 2nd section= 0.234 ohm
resistance of 3rd section= 0.176 ohm
resistance of 4th section= 0.132 ohm
resistance of 5th section= 0.099 ohm
resistance of 6th section= 0.074 ohm
resistance of 7th section= 0.056 ohm
resistance of 8th section= 0.042 ohm


## Example Number 30.54, Page Number:1083¶

In [164]:
import math
from sympy.solvers import solve
from sympy import Symbol
#variable declaration
n=Symbol('n')
v=500#V
z=20
ra=1.31#ohm
t=218#N-m
ratio=1.5
slot=60
phi=23*0.001#Wb

#calculation
ia=t/(0.159*phi*slot*z)
i1=ia*ratio
i2=ia
k=i1/i2
r1=v/i1
n=solve(k**(n-1)-(r1/ra),n)
r2=r1/k
r3=r2/k
r4=r3/k
p1=r1-r2
p2=r2-r3
p3=r3-r4
p4=r4-ra

#result
print "resistance of 1st section=",round(p1,3),"ohm"
print "resistance of 2nd section=",round(p2,3),"ohm"
print "resistance of 3rd section=",round(p3,3),"ohm"
print "resistance of 4th section=",round(p4,3),"ohm"

resistance of 1st section= 2.237 ohm
resistance of 2nd section= 1.491 ohm
resistance of 3rd section= 0.994 ohm
resistance of 4th section= 0.678 ohm


## Example Number 30.55, Page Number:1084¶

In [165]:
#variable declaration
v=440#V
drop=0.02
efficiency=0.95
i_per=1.30

#calculation
i1=i_per*il
vd=drop*v
rm=vd/il
r1=v/i1
r=(r1-rm)/6

#result
print "resistance of each rheostat=",r,"ohm"

resistance of each rheostat= 0.615721729566 ohm


## Example Number 30.56, Page Number:1085¶

In [170]:
#variable declaration
v=650.0#V
r=0.51#ohm
i1=140.0#A
i2=100.0#A
per=0.20

#calculation
ratio=i1/i2
r1=v/i1
r2=((per+1)/ratio-per)*r1
r3=(per+1)*r2/ratio-per*r1
r4=((per+1)*r3/ratio)-per*r1

p1=r1-r2
p2=r2-r3
p3=r3-r4

#result
print "number of steps=",3
print "resistance of 1st section=",round(p1,3),"ohm"
print "resistance of 2nd section=",round(p2,3),"ohm"
print "resistance of 3rd section=",round(p3,3),"ohm"

number of steps= 3
resistance of 1st section= 1.592 ohm
resistance of 2nd section= 1.364 ohm
resistance of 3rd section= 1.17 ohm

In [ ]: